Skip to main content

Full text of "Analytical Mechanics"

See other formats


EQUILIBRIUM OF RIGID BODIES
position of the rod is given by sin 8 =
a — b
:, where B is the angle it
makes with the plane of the brim of the bowl which is horizontal.
14.   Prove that when a rigid body is in equilibrium under the action of three forces their lines of action lie in the same plane and intersect at the same point.
15.   Find the forces which tend to compress or extend the different members of the following cranes.
1,750 .Ibs,
16. Supposing the weights of the following figures to be in equilibrium find their relative magnitudes. The circles which arc tangent to other •circles represent gears.
64.  Resultant of a System of Forces Acting upon a Rigid Body.
—We have already shown that the most general displacement of a rigid body consists of a translation along, and a rotation about, a certain line. Therefore such a displacement can be prevented by a single force opposed to the translation and a single torque opposed to the rotation. Thus a single force and a single torque can be found which will keep a rigid body in equilibrium against the action of any system of forces.